EX. Evaluate the JoJex*+2xy+y*) dydx when step size of X = 0-2 and step size of y=o.5?

Q: 4. Evaluate fe fds where f(r, y, z) , ) and 0 <t< 1. = 12r2 and the path C is given by r(t)

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Q: EX. Use Euler's method (moditied) t appro y' = x+y for y C1) = 1 ; h =0.1,13XL2 Ư the açcuracy of E…

A: According to the given information it is required to approximate y'=x2+y for y(1)=1, h=0.1, 1≤x≤2

Q: Evaluate I = √x+e²×¯¹dx 2x-1 a) By using Trapezoidal rule with 12 segments b) By using Simpson's one…

A: The given integral is I=∫17x+e2x-1dx. To Evaluate: (a) Using Trapezoidal Rule with 12 segments. (b)…

Q: Juneten and be fure at lebel aut least thre f (n) : Su

A: As asked we can find the answer as below

Q: Grplain why Ž diverges, 27 41 even though has a finite liniit 2 t 2

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Q: if x~unif. (0,2),find the U.b. of p(lx - mul>= 2)

A: Given X~Unif(0,2) Result: if X~unif(a,b) then  Mean=(a+b)/2 Variance=(b-a)2/12

Q: Evaluate S, 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant.

A: we need to evaluate the integration over the region using the triple integral. First we will find…

Q: Y=√x, but is shifted to the right 1unit y =

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Q: dy ({})y+3

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Q: alue of the pur C: |z| = (:-1)(z-

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Q: for which the sys y +z = 6, 4x + Ay = -5 has infinitely m a root of which qu: %D :

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Q: find the Solehion dy'= 4t + 2e

A: Given the differential equation :

Q: (b) In(2x2 + у — 23) %3D х

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Q: Let y1 = 9cos(2x) and y2 = 2cos2 (x) – 2sin? (x). Calculate the Wronskian, W(y1, Y2). Give your…

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Q: -8 6. Evaluate the integral +y² dydx

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Q: Consider the figure below. uestion 1 T. 2x W Зх - 5 Previous

A: Given TW= 2x, 3x-5

Q: Save the following Sef of Lincay equations using over relaxoation 10X, +X2 + X3 12 X, + 10X2 + X3 =…

A: Rewrite the given system of equations, to find x1, x2 and x3. Multiply each right hand side…

Q: . Show that z)= E kz is D: 1215 continuous io domain

A: The series can be shown as continuous in a domain if it converges. Therefore, the first calculate…

Q: (a) Suppose x E Q with x # 0 and y E R – Q. Show that their product ry is irrational.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: A nermally distolated cndee erióbh with medn e has ė pabiblity dansty pabibiliy Ancty fnctin fris by

A: The normal distribution: A continuous random variable X is said to follow normal distribution if the…

Q: Q4/is that, the Sulutton to the differentiel equation dy-tX+4. is it's

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Q: Use Greens Theorem to evalute fyx² dx + x²dy as shown below Leh Half of (0,5) +y-25 (0,-5)

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Q: Assume w = ts³, 4ts) and (x,y) = 6xy of (х.у) - 4х Find as when t = s = 1 %3D

A: Given: From the given expression it is clear that 'f' is a function of 'x' and 'y', and 'x' and 'y'…

Q: [5] Use the Gaussian quadrature to approximate the integral 1 x²e¬*dx. (a) Choose n = (b) Choose n =…

A: As per instruction we are allowed to answer only two sub questions. The generalised Gaussian…

Q: A natural cubic spline S on [0,2] is defined by (So(x) = 1+ 2x – x³ S(x) = Is, (x) = a + b(x – 1) +…

A: Given: Natural cubic spline S on [0,2] is defined as: Sx=S0x=1+2x−x3 if 0≤x≤1S1x=a+bx−1+cx−12+dx−13…

Q: X+ xy B. Evaluafe the tripe in tagral S5* xy dydzdx,

A: As we know that: The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 (B). From the given integration:…

Q: 9 Give with an not example of T: W≤X →Y, to XT Ext. .R. boundedag. - keše bes

A: Please find the solution innext step this is an non-example of Tietze extension theorem in Topology.

Q: show that the Pio Diophant ine equation 2x -5y= | has no integer Selutions .

A: Given, 2x²=1+5y² Here 5y2 is a multiple of 5 ending in digit 5 or 0. 2x2 can end in 1 or 6 But no…

Q: becB.2. Evaluatte fhe vpperbound for R,(X) G0 for fulecosx

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Q: of fxyl = 3X-y+6 Subjected QI Find to x+y=4 extrume v alues

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Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

Q: H.W. a PDE from the followi'ng- @u=f() Form メツ 0u=fcx?ー)

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Q: (D² -1)y = 2(1-e-2x)-1/2

A: Given that (D2-1)y=2(1-e-2x)-12

Q: t DR) dende Dartine dövßes e te than show that Deo) X DR1) to DG20). o is atoxphic

A: To show D20×D21 is isomorphic to D420: Define a map f:D20×D21→D420 by fa,b=a×b a×b∈D420: Suppose a…

Q: firved さ。 rom the follow fallowsiy fuetiong X3 らt2X+ xて y2 フ

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Q: 03) find the ax en the sl abetwed wol y=J2-X, and y= 0

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Q: lestion 25 Consider the following IVP: y" + 3y' + 2y = 12x?; y(0) = a, y'(0) = b

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Q: finde general Sonotion 1- y' = See'y 2X-1 %3D 2- 3-Xy=Y+2x $ in?

A: This question can be solved by applying the concept of differential equation.

Q: 5. If 4=2xy į +3x°y -3pyzk is solenoidal at(1,1.1). Find p.

A: DivA=0

Q: IF Y = u²-1 u²+1 Find dy np

A: Given,  y=u2-1u2+1

Q: -x -e = luxe by Bisection Slove:.

A: To solve by using the bisection method.

Q: 2 I| ysin(xy)dydx Н.W.

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Q: D Reduce the Q.F 22,xz t 22,X3 2ズュズ3 weag ayf of oothogonal toans fermation by an Ans: y+92-295

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Q: Use the TRAPEZOIDAL with 3 level Romberg (k = 3) to evaluate: e* sin x , 1+x²

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Q: Consider the systenm o o-21 x + %3D 0 3 Frnel the ennit s tep esponse of the system.

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Q: 16.1. Use an antiderivative to show that for every extending from a point 21 to a point 22 2" dz =…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.